The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  1  1  1  X  1
 0  X  0  0  0  0  0  X  X  X 3X  0  X 3X  X 3X 2X 2X  0 3X  0 4X  0 4X 2X 2X  X  X 3X 3X  0  X  X 4X 2X  0  X 4X
 0  0  X  0  0  0  X 3X 3X 2X 2X 2X 4X  0 2X 4X 3X 2X 3X  0  0 4X 2X 3X  X  0 3X 4X  0  0  X  X 4X  0  0  X  X 3X
 0  0  0  X  0  0 3X 4X 3X 3X 3X 4X 3X  X 4X 2X 4X  0  0 2X 3X 2X 2X  0 4X  X 2X  0 4X  0 2X 3X 4X 3X 2X  X 3X 4X
 0  0  0  0  X  0 3X  0 2X 3X  X 2X  0 3X  X  X 3X  0 4X 3X 3X 3X  X 4X  0  0 3X  X  X 3X 4X  X 2X 3X 3X  X 4X 4X
 0  0  0  0  0  X 3X  X 2X  0 3X 4X 4X 4X 2X 4X 2X  X 3X 2X 2X  X 3X 2X 3X 4X 4X 4X 3X 3X  X  X  0 4X  0 3X 3X 2X

generates a code of length 38 over Z5[X]/(X^2) who´s minimum homogenous weight is 125.

Homogenous weight enumerator: w(x)=1x^0+300x^125+784x^130+1084x^135+100x^136+1604x^140+1600x^141+1672x^145+9600x^146+2256x^150+25600x^151+2300x^155+25600x^156+2408x^160+1668x^165+968x^170+448x^175+116x^180+8x^185+8x^190

The gray image is a linear code over GF(5) with n=190, k=7 and d=125.
This code was found by Heurico 1.16 in 13 seconds.